| C2有理插值样条曲线曲面 |
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| 引用本文： | 方逵,朱国庆.C2有理插值样条曲线曲面[J].国防科技大学学报,1996,18(3):147-151. |
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| 作者姓名： | 方逵 朱国庆 |
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| 作者单位： | 国防科学技术大学系统工程与数学系 |
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| 基金项目： | CAD／CG国家重点实验室资助 |
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| 摘 要： | 首先提出一组基函数向量,它具有以下特定的性质：ＢＢ（０）Ｔ＝（０．０,１．０,０．０,０．０）,ＢＢ（１）Ｔ＝（０．０,０．０,１．０,０．０）ＢＢ＇（０）Ｔ＝（－０．５,０．０,０．５,０．０）,ＢＢ＇（１）Ｔ＝（０．０,－０．５,０．０,０．５）ＢＢ″（０）Ｔ＝－（１．０,－２．０,１,０,０．０）,ＢＢ″（１）Ｔ＝（０．０,１．０,－２．０．１．０）。进而研究了以此函数向量的张量积形式定义的有理样条曲面。并得以下结论：（１）插值性;（２）Ｃ２连续性;（３）局部性和可调性。文中还分析了“权”的作用,并指出它与三次Ｂ－样条的类似性。
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| 关 键 词： | 有理样条曲线 有理样条曲面 插值曲线曲面 |
| 收稿时间： | 1/9/1996 12:00:00 AM |
C2 Rational Biquitic Interpolation Surface |
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| Fang Kui and Zhu Guoqing.C2 Rational Biquitic Interpolation Surface[J].Journal of National University of Defense Technology,1996,18(3):147-151. |
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| Authors: | Fang Kui and Zhu Guoqing |
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| Abstract: | We first present a vector of function basis BB (t) that satisfied BB(0)T=(0. 0,1. 0,0. 0,0. 0), BB(1)T= (0. 0,0. 0, 1. 0,0. 0) BB' (0)T= (-0. 5,0. 0,0. 5,0. 0), BB'(1)T=(0. 0, -0. 5,0. 0,0. 5) BB"(0)T= (1. 0. -2. 0,1. 0,0. 0), BB"(1)T=(0. 0,1. 0, -2.0,1. 0) Secondly we discuss the rational surface defined in tension-product form using above function vector BB (t). The interpolation surface implies the following results: (1) The surface interpolates control points; (2) It is second order parametrically continuous;(3) It is local and can be adjusted by weights. The effect of weights is also analysed and has similar result as bicubic rational B-spline surface. |
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| Keywords: | rational spline curve rational spline surface interpolation curve surface |
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